臺灣博碩士論文加值系統

現今投影機相關產業受惠於視訊與影音技術之突破而蓬勃發展，但是光機產生的廢熱儼然成為設計挑戰，受限於光機外形結構，唯採用離心式風扇才能克服系統流阻並供給所需風量，相關風扇選用則必頇藉由風扇性能曲線匹配系統流阻來決定。針對投影機散熱需求，本文選定小型前傾式離心風扇做為研究標的。然而，現行數值模擬方法無法在風扇開發初期正確計算出與量測結果相接近之性能曲線，為改善當前預測風扇特性準確性較低之缺點，本研究使用計算流體動力學(Computational Fluid Dynamics, CFD)軟體STAR-CD，發展出一套有別於傳統方法之計算程序，該方法將AMCA標準量測設備內噴嘴的阻抗曲線以下游離散式多孔性阻抗區的模式導入計算模型，並據此稱為DFR方法(downstream flow resistance)。求解過程中，DFR方法將阻抗區上下游的靜壓差轉換成阻抗動量源併入動量守恆方程式，遵循噴嘴阻抗約束方程反覆運算壓力和流速等計算變量，確保通過阻抗區之流量與阻抗區上下游的靜壓差滿足噴嘴阻抗關係式，並使風扇出口靜壓值更接近實際情況。經比對依照AMCA標準程序實驗所量測的風扇特性，發現採用DFR方法可將預測結果的精確度提高至97%以上，然而傳統方法計算模擬的最大誤差卻高達62%。此外，使用DFR方法搭配靜態網格和動態網格所計算的性能曲線幾乎一致，這將有助於風扇設計者以DFR方法與靜態網格縮短產品開發時程。當背壓升高時，蝸殼出口區由傳統方法所計算的流速分佈明顯受堵無法順利流出轉而趨向舌部，這表示傳統方法未能正確計算風扇流場，導致預測流量值偏低，比對由DFR方法模擬之流場則無此現象並較為正確。

The progress in the video related technologies fueled the projector industry to a flourish. However, heat dissipations from the optical engine became a design challenge. The fan selection for lamp cooling must be designed according to the interaction between fan performance curve and system impedance. Unfortunately, the existent simulation methods cannot predict the fan curve close to the measured results during the design stage. To improve the obvious defects of conventional methods, a newly developed computational approach by using the commercial code (STAR-CD) of computational fluid dynamics is employed. The main purpose is to study the fan flow and performance curve of the forward-curved blades centrifugal fan. The new approach, which is termed the “downstream flow resistance” (DFR) method, engaged the flow resistances of nozzles of the AMCA test rig in the downstream area of the computational domain. The engaged flow resistance is treated as the distributed momentum sources in a specific porous region. The static pressure at the fan exit is iteratively corrected to real values. By using the DFR method, the maximum deviation of the calculated fan curve from the measured results can attain a level less than 3%. This progress presents a dramatic improvement over the maximum deviation of about 62% obtained by using the conventional method. The improvement is due to the appropriate prediction of the fan flow by properly adjusted pressure drops across the porous region. Future designers will benefit from the high accuracy of fan performance prediction and shorter design cycle time by utilizing the DFR method with the static-grid scheme.

摘要 .........................................................................i
英文摘要 ....................................................................ii
誌謝 .......................................................................iii
目錄 ........................................................................iv
符號索引 ....................................................................xi
表圖目錄 ....................................................................xv第一章 緒 論..................................................................1
1.1 研究動機 .................................................................1
1.2 文獻回顧 .................................................................4
1.3 研究目的 ................................................................16
第二章 計算方法..............................................................18
2.1 研究標的 ................................................................18
2.1.1 風扇結構 ..............................................................18
2.1.2 風扇標稱性能 ..........................................................19
2.2 計算流力求解軟體 ........................................................19
2.3 統御方程式 ..............................................................21
2.4 下游流阻法( DFR Method) .................................................23
2.5 紊流模式 ................................................................25
2.6 計算模型 ................................................................28
2.6.1 網格結構 ..............................................................28
2.6.2 網格獨立性分析 ........................................................28
2.6.3 模型比較 ..............................................................29
2.7 數值求解方法 ............................................................31
2.7.1 離散化方程式 ..........................................................31
2.7.2 時間離散 ..............................................................33
2.7.3 離散差分法 ............................................................33
2.7.4 求解演算法 ............................................................33
2.7.5 收斂標準 ..............................................................34
第三章 風扇性能量測實驗 .....................................................36
3.1 實驗方法 ................................................................36
3.2 實驗設備 ................................................................37
3.3 實驗量測不準度 ..........................................................38
3.4 風扇流量計算 ............................................................39
3.4.1 大氣空氣密度(Atmospheric air density) .................................39
3.4.2 腔室空氣密度(Chamber air density) .....................................40
3.4.3 風扇空氣密度(Fan air density) .........................................40
3.4.4 空氣動力黏滯係數(Dynamic air viscosity) ...............................41
3.4.5 噴嘴靜壓比(Alpha ratio) ...............................................41
3.4.6 噴嘴直徑比(Beta ratio) ................................................41
3.4.7 擴張係數(Expansion factor) ............................................41
3.4.8 雷諾數(Reynolds number) ...............................................42
3.4.9 噴嘴流量係數(Nozzle discharge coefficient) ............................42
3.4.10 腔室噴嘴流量(Airflow rate for chamber nozzles) .......................42
3.4.11 風扇流量(Fan airflow rate) ...........................................42
第四章 風扇性能曲線之模擬與實驗結果 .........................................43
4.1 風扇性能模擬之誤差 ......................................................43
4.2 軸流扇與離心扇之性能差異 ................................................43
4.3 風扇性能計算與實驗量測比較 ..............................................44
4.4 實驗與計算之壓力係數及流量係數 ..........................................46
4.4.1 靜壓係數(Static pressure coefficient) .................................47
4.4.2 總壓係數(Total pressure coefficient) ..................................47
4.4.3 流量係數(Flow coefficient) ............................................47
第五章 零靜壓時的流場與壓力場 ...............................................49
5.1 葉片間流道出口之流量分佈 ................................................49
5.2 葉片間沿流道之面平均靜壓變化 ............................................51
5.3 葉面在不同高度位置之靜壓變化 ............................................52
5.4 沿渦捲流道通過徑向截面之流量變化 ........................................54
5.5 沿渦捲流道徑向截面平均靜壓之變化 ........................................54
5.6 不同葉輪圓周角度沿蝸殼內壁高度之靜壓變化 ................................55
5.7 旋轉葉柵間流體之相對速度與流線 ..........................................56
5.7.1 旋轉葉柵間傳統靜態網格法計算之相對流速與流線 ..........................57
5.7.2 旋轉葉柵間DFR靜態網格法計算之相對流速與流線. ..........................59
5.7.3 旋轉葉柵間DFR動態網格法計算之相對流速與流線. ..........................61
5.8 旋轉葉柵間流體之靜壓分佈 ................................................63
5.8.1 旋轉葉柵間傳統靜態網格法計算之靜壓分佈 ................................63
5.8.2 旋轉葉柵間DFR靜態網格法計算之靜壓分佈 .................................65
5.8.3 旋轉葉柵間DFR動態網格法計算之靜壓分佈 .................................67
5.9 流體位於蝸殼內部橫向截面的速度與流線 ....................................69
5.9.1 傳統靜態網格法於蝸殼內部橫向截面計算之絕對流速與流線 ..................69
5.9.2 DFR靜態網格法於蝸殼內部橫向截面計算之絕對流速與流線 ...................70
5.9.3 DFR動態網格法於蝸殼內部橫向截面計算之絕對流速與流線 ...................72
5.10 流體位於蝸殼內部橫向截面的靜壓分佈 .....................................73
5.10.1 傳統靜態網格法於蝸殼內部橫向截面計算之靜壓分佈 .......................73
5.10.2 DFR靜態網格法於蝸殼內部橫向截面計算之靜壓分佈 ........................75
5.10.3 DFR動態網格法於蝸殼內部橫向截面計算之靜壓分佈 ........................77
第六章 Ps = 29.52 Pa時的流場與壓力場 ........................................80
6.1 葉片間流道出口之流量分佈 ................................................80
6.2 葉片間沿流道之面平均靜壓變化 ............................................81
6.3 葉面在不同高度位置之靜壓變化 ............................................82
6.4 沿渦捲流道通過徑向截面之流量變化 ........................................84
6.5 沿渦捲流道徑向截面平均靜壓之變化 ........................................85
6.6 不同葉輪圓周角度沿蝸殼內壁高度之靜壓變化 ................................85
6.7 旋轉葉柵間流體之相對速度與流線 ..........................................86
6.7.1 旋轉葉柵間傳統靜態網格法計算之相對流速與流線 ..........................86
6.7.2 旋轉葉柵間DFR靜態網格法計算之相對流速與流線............................88
6.7.3 旋轉葉柵間DFR動態網格法計算之相對流速與流線............................90
6.8 旋轉葉柵間流體之靜壓分佈 ................................................92
6.8.1 旋轉葉柵間傳統靜態網格法計算之靜壓分佈 ................................92
6.8.2 旋轉葉柵間DFR靜態網格法計算之靜壓分佈 .................................94
6.8.3 旋轉葉柵間DFR動態網格法計算之靜壓分佈 .................................97
6.9 流體位於蝸殼內部橫向截面的速度與流線 ....................................99
6.9.1 傳統靜態網格法於蝸殼內部橫向截面計算之絕對流速與流線 .................100
6.9.2 DFR靜態網格法於蝸殼內部橫向截面計算之絕對流速與流線 ..................101
6.9.3 DFR動態網格法於蝸殼內部橫向截面計算之絕對流速與流線 ..................103
6.10 流體位於蝸殼內部橫向截面的靜壓分佈 ....................................104
6.10.1 傳統靜態網格法於蝸殼內部橫向截面計算之靜壓分佈 ......................104
6.10.2 DFR靜態網格法於蝸殼內部橫向截面計算之靜壓分佈 .......................108
6.10.3 DFR動態網格法於蝸殼內部橫向截面計算之靜壓分佈 .......................112
第七章 Ps = 62.52 Pa時的流場與壓力場 .......................................116
7.1 葉片間流道出口之流量分佈 ...............................................116
7.2 葉片間沿流道之面平均靜壓變化 ...........................................118
7.3 葉面在不同高度位置之靜壓變化 ...........................................119
7.4 沿渦捲流道通過徑向截面之流量變化 .......................................122
7.5 沿渦捲流道徑向截面平均靜壓之變化 .......................................123
7.6 不同葉輪圓周角度沿蝸殼內壁高度之靜壓變化 ...............................123
7.7 旋轉葉柵間流體之相對速度與流線 .........................................125
7.7.1 旋轉葉柵間傳統靜態網格法計算之相對流速與流線 .........................125
7.7.2 旋轉葉柵間DFR靜態網格法計算之相對流速與流線 ..........................126
7.7.3 旋轉葉柵間DFR動態網格法計算之相對流速與流線 ..........................128
7.8 旋轉葉柵間流體之靜壓分佈 ...............................................129
7.8.1 旋轉葉柵間傳統靜態網格法計算之靜壓分佈 ...............................129
7.8.2 旋轉葉柵間DFR靜態網格法計算之靜壓分佈 ................................132
7.8.3 旋轉葉柵間DFR動態網格法計算之靜壓分佈 ................................134
7.9 流體位於蝸殼內部橫向截面的速度與流線 ...................................136
7.9.1 傳統靜態網格法於蝸殼內部橫向截面計算之絕對流速與流線 .................136
7.9.2 DFR靜態網格法於蝸殼內部橫向截面計算之絕對流速與流線 ..................138
7.9.3 DFR動態網格法於蝸殼內部橫向截面計算之絕對流速與流線 ..................140
7.10 流體位於蝸殼內部橫向截面的靜壓分佈 ....................................142
7.10.1 傳統靜態網格法於蝸殼內部橫向截面計算之靜壓分佈 ......................142
7.10.2 DFR靜態網格法於蝸殼內部橫向截面計算之靜壓分佈 .......................145
7.10.3 DFR動態網格法於蝸殼內部橫向截面計算之靜壓分佈 .......................148
第八章 流場與壓力場於不同背壓之變化 ........................................152
8.1 葉柵間流道出口之流量分佈於不同背壓之變化 ...............................152
8.2 葉柵間沿流道的面平均靜壓於不同背壓之變化 ...............................152
8.3 葉面靜壓分佈於不同背壓之變化 ...........................................153
8.4 渦捲流道徑向截面之流量分佈於不同背壓之變化 .............................154
8.5 渦捲流道徑向截面平均靜壓於不同背壓之變化 ...............................154
8.6 蝸殼壁面靜壓於不同背壓之變化 ...........................................155
8.7 旋轉葉柵間相對速度流場於不同背壓之變化 .................................155
8.8 旋轉葉柵間流體靜壓分佈於不同背壓之變化 .................................157
8.9 蝸殼內部橫向截面的絕對速度流場於不同背壓之變化 .........................158
8.10 蝸殼內部橫向截面的靜壓分佈於不同背壓之變化 ............................159
第九章 DFR方法於軸流扇性能曲線之模擬 .......................................161
9.1 DFR方法於單級軸流式風扇性能模擬 ........................................161
9.2 DFR方法於不同葉片攻角對單級軸流式風扇性能模擬 ..........................162
9.3 DFR方法於多級軸流式風扇性能模擬 ........................................162
第十章 結論與建議 ..........................................................164
10.1 結論...................................................................164
10.2 建議...................................................................166
參 考 文 獻.................................................................167

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